Question

The height h, in feet, at some time t, in seconds, of an object propelled upward at a speed of 112 feet per second from an initial height of 31 feet is given by the function h(t)=-16t^(2)+112t+31 a

Answer 1

Explanation:

he term -16t^2 represents the effect of gravity on the object's height. Since gravity pulls objects downward, the coefficient -16 indicates that the object is moving upward initially but eventually slows down and starts falling back down due to the effect of gravity.

2. The term 112t represents the upward velocity of the object. It indicates that the object is propelled upward at a constant speed of 112 feet per second.

3. The constant term 31 represents the initial height of the object. This is the height at t = 0, which is the starting point of our time frame.

By plugging in different values of t into the function, we can calculate the height of the object at those specific times. For example, if we want to find the height at t = 2 seconds, we substitute t = 2 into the function:

h(2) = -16(2)^2 + 112(2) + 31

= -16(4) + 224 + 31

= -64 + 224 + 31

= 191 feet

Therefore, at t = 2 seconds, the object would be at a height of 191 feet.

The function allows us to track the object's height at any given time during its flight based on the initial height, upward velocity, and the effect of gravity.